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SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
Recall the distance formula: \[d^2=(xx_0)^2+(yy_0)^2\] In this particular problem, you have \((x_0,y_0)=(0,0)\) (the origin), since you want to find the distance between any given point on the curve \((x,y)\) and the origin. \[d^2=x^2+y^2\] Substitute the given equation of the curve: \[d^2=x^2+\left(4\sqrt{2x+2}\right)^2\\ d^2=x^2+16(2x+2)\\ d^2=x^2+32x+32\] Now differentiate both sides implicitly with respect to some dummy variable \(t\): \[2d\frac{dd}{dt}=(2x+32)\frac{dx}{dt}\] You're told that at the point \((1,8)\), \(x\) is increasing at a rate of 3 units/s, which translates to \(\dfrac{dx}{dt}=3\). \[2d\frac{dd}{dt}=(2\cdot1+32)(3)\\ 2d\frac{dd}{dt}=102\] You're asked to find \(\dfrac{dd}{dt}\), so first you need to find \(d\). To do this, find the distance between \((1,8)\) and \((0,0)\), then plug it into the above equation. Lastly, solve for \(\dfrac{dd}{dt}\).
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@SithsAndGiggles omg thank you!! :)
 11 months ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
Yer welkum
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@SithsAndGiggles hey, i found the distance which is 8 right? then i plugged in 8 into the equation and got 51/8... however, something is wrong?
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
i get \(\frac{19}{8}\)
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
oh nvm i got it.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
it's 6.32577
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
to find the distance is this:
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i got it... thank you! @satellite73
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
\[d^2=x^2+32x+32\] \[2dd'=2xx'+32x'\] \[dd'=xx'+32x'\] \[8d'=3+96\]
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
oh right doh
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
distance isn't 8 is it? distance is \(\sqrt{65}\)
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
which is pretty close to 8...
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
is the final answer \(\frac{99}{\sqrt{65}}\) ?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
close yes... i thought i had to do this: x2x1/y2y1
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
it's 51/sqrt(65)/65
 11 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
oh damn i forgot to divide 32 by 2 must be past my bedtime
 11 months ago
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